\chapter{Analytic trigonometry}

    \section{Law of sines}
    
    


 Check your understanding 



Answer the questions.
\begin{enumerate}
\item 
State the Law of Sines.

\item
Decide if the following problem can be solved with the Law of Sines, and if they can, determine the case.


    

  1. 
\(A\), \(a\), \(B\) given
    2. 


  2.  \(B\), \(a\), \(c\) given
    3. 


  3.  \(A\), \(C\), \(b\) given
    4. 


  4.  \(C\), \(a\), \(c\) given 
    5. 


  5.  \(B\), \(b\), \(c\) given 
    6. 



\item
Suppose we are solving a triangle with the Law of Sines and we find it is a ASA case with one angle
\(95^\circ\) and the other angle \(88^\circ\). Is there a solution?

\item
In a SSA case, we are given \(a\), \(A\) and \(b\), and we found that \(b/a=2.2\). If \(A=30^\circ\),
is there a solution?

\item
In the previous problem, suppose now that \(A=20^\circ\). How many solutions are there?
\end{enumerate}






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